The idea of using non-covex regularization with “maximizing concavity” in a convex problem
has been illustrated in [1]},
wherein the quadratic formulation of data fidelity term can be used to compensate the non-convexity
in the regularization so that the objective function is still convex.
In this work, we adopt this idea for an extraction algorithm with simultaneous denoising.
Entirely there are three regularizers in (REF ),
and we allow one of them to be non-convex to promote the global sparsity more strongly.
Moreover, the specific condition to assure the convexity of problem (REF ) is derived as the following proposition.
